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A detailed tutorial on the absolute value of a complex number. Step by step tutorial including several examples on the absolute value of a complex number for reference.

The absolute value of a complex number is a little different than the absolute value of a real number, because complex numbers deal with imaginary numbers. However, the answer is still a non-negative real number, just like the numbers you deal with in other math classes every day. Say that a complex number z is equal to a + bi, where i is an imaginary number. The |z| is equal to the square root of a^2 plus b^2. In other words, square both a and b, add them together, and find the square root in order to have to absolute value of a complex number z.

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A detailed tutorial on how to identify a perfect square. Step by step tutorial including several examples of how to identify perfect squares for reference.

A perfect square is a number that is the square of a non-negative integer – in other words, a positive whole number. The way you can identify a perfect square is that when you take the square root, you should not end up with a fraction or decimal – you should get the non-negative integer. There are many perfect squares, but most of them are large numbers, so many people do not know more than the squares of the numbers one through twelve.

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A detailed tutorial on negative square roots. Step by step tutorial including several examples of negative square roots for reference.

Negative square roots are just like negative numbers. Just like positive and negative numbers have the same true value, only on opposite sides of the number line, negative square roots and positive square roots also have that same property. However, they should not be confused with the square root of a negative number. The square root of a negative number is known as an imaginary number, and is not used in basic algebra. The negative square root is expressed by the square root of a number, with a negative sign in front of the square root symbol, and the square root of a negative number is expressed as a negative number with a square root symbol placed over it.

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A detailed tutorial on the definition of the index of a radical expression. Step by step tutorial including several examples of the index of a radical expression for reference.

A radical expression is what most people know as a square root. The number, variable, or expression inside the square root symbol is referred to as the radicand. What some of you may not realize is that not only are there square roots, there are cube roots, and several other types of roots. These are the exact opposite functions of the exponents. A square root should technically have a little number two on the outside left of the square root symbol. A cube root would have a three there – any number can go there. That is the index.